The Tube That Was Not Broken: Lorenz and the Three Decimals of 1961
In 1961 Edward Lorenz rounded a number from six decimals to three and his weather model changed its sky. It was no fault: it was deterministic chaos.
In the winter of 1961, at MIT, the meteorologist Edward Lorenz was running a small weather model on a Royal McBee, a slow, noisy computer full of vacuum tubes. The model had twelve variables, things like temperature and wind speed, and it printed months of weather that had never existed. One day Lorenz wanted to look at a sequence at greater length. Instead of starting over, he took a shortcut: he typed in by hand the numbers from a line printed midway through the earlier run, started the machine and went for a cup of coffee.
He came back about an hour later. He expected a copy of the weather he had already seen. He found another sky. The two series began almost the same and then drifted apart, until after a few simulated months they had nothing left in common.
The tube that was not broken
His first suspect was the most fragile object in the room: a vacuum tube, a glass envelope with a glowing filament, that had failed. In the computers of the time it was the obvious fault. But the machine was working. The error was in the numbers. In memory the computer kept six decimal places, for instance 0.506127; to save space the printout showed three, 0.506. Lorenz had entered the rounded values, assuming a difference of one part in a thousand did not matter. It did. That tiny difference grew at every step until it dominated the whole result.
I like that the suspect was the tube. It is the reflex of anyone who works with machines: when the result betrays you, you look for the broken part. Here the part was intact, and the betrayal lay in the system's very faithfulness. A fully deterministic model, with no chance and no faults, carried out its rules to the letter and for that very reason amplified the gap it had been handed.
One part in a thousand
From that coffee break came what we now call chaos theory. In 1972 Lorenz presented a paper whose title became proverbial: "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" For meteorology the consequence was sober and severe: it may be impossible to predict the weather with reasonable accuracy beyond two or three weeks. Not for lack of computing power, but because of the nature of the system itself.
The site has a tool that repeats the experiment on a small scale. The Chaotic Triple Pendulum simulates three masses hanging from three rods and, if you switch on the ghost copies, starts them identical except for one angle shifted by a thousandth of a radian. For a few moments the pendulums overlap. Then one hesitates, the other carries on, and the trails part for good. It is Lorenz's same thousandth, seen in motion.
There is a lesson here for every simulation, one the essay Reality Through Interfaces takes seriously: a model is not the world, it is a transcription of it, and every transcription rounds off. The problem is not the rounding, which is unavoidable. It is forgetting where you did it. Lorenz found it because he looked harder at the numbers instead of replacing the tube.
That tube, intact, deserves a place in some imaginary museum of innocent machines. It had done nothing wrong. It had only obeyed, and in obeying it showed that the future cannot be printed to three decimal places.
Sources: Circa January 1961: Lorenz and the Butterfly Effect, APS News; When the Butterfly Effect Took Flight, MIT Technology Review; Edward Lorenz, father of chaos theory and butterfly effect, dies at 90, MIT News (accessed 22 October 2026).
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